On the comparison principle and existence results for terminal value problems

  • Zahia Drici
  • J. Vasundhara Devi
  • Farzana McRae

Abstract

In this paper we give a brief survey of results dealing with the comparison principle and existence results for terminal-value problems (TVP). We begin with terminal differential inequalities, existence of extremal solutions and the corresponding comparison principle, for ordinary differential equations (ODE), and discuss the method of lower and upper solutions for ODE. We then present an important extension of this basic theory, which relaxes the strong assumption that $v(t)\leq u(t)\mf t\in
[a,b]$, where $v(t)$ and $w(t)$ are lower and upper solutions, respectively. Next, we state results pertaining to TVP for impulsive ODE and then give parallel results for fractional differential equations.

Published
2014-05-25
Section
Articles